The Definition of Points
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From: Virgil on 31 Mar 2007 21:59 In article <460f00a0(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Look back. The nth is equal to n. Inductive proof holds for equality in > the infinite case Not in vN. And inductive proofs do not work that way. One can prove by induction that something is true for each natural, but that does not create any infinite naturals for which it is true.
From: Virgil on 31 Mar 2007 22:01 In article <460f0317(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > There are not zero, nor any finite number of reals in (0,1]. There are every finite and more of reals in (0,1].
From: Tony Orlow on 31 Mar 2007 22:03 Lester Zick wrote: > On Fri, 30 Mar 2007 12:42:06 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>>> It's universally meaningless in isolation. not(x) simply means >>>>>> "complement of x" or "1-x". You assume something else to begin with, >>>>>> which is not demonstrably true. >>>>> No I don't, Tony.I demonstrate the universal truth of "not" per se in >>>>> mechanically exhaustive terms through finite tautological reduction to >>>>> self contradictory alternatives which I take to be false to the extent >>>>> they're self contradictory. If you want to argue the demonstration per >>>>> se that's one thing but if you simply want to revisit and rehash the >>>>> problem per say without arguing the demonstration per se that's >>>>> another because it's a problem per say I have no further interest in >>>>> unless you can successfully argue against the demonstration per se. >>>>> >>>> not(not("not not")) >>>> >>>> "not not" is not self-contradictory-and-therefore-false. >>> Well, Tony, let me ask you. If "not not" were self contradictory would >>> you agree with me that "not" would be true of everything inasmuch as >>> it would represent the tautological alternative to and the exhaustion >>> of all possibilities for truth between "not" and "not not"? >> If "not not" were demonstrated to be a statement > > "To be a statement"? What makes it not a statement? > It no predicate. (fine, read "is" into that if you like, but be aware you're implying a predicate that's not stated...) >> that implied its own >> negation then "not not not" would have to be true, but it's only >> equivalent to "not" in the normal usage of "not", which doesn't make >> "not not" constitute a statement. > > Oooooookay then. Moving right along to the next true or not true > compounding of "not". > not. but, anyway... >>> Because I mean there are probably people out there who wouldn't agree >>> self contradiction is false hence tautological alternatives must be >>> true so I wouldn't know how to approach the demonstration of truth >>> with such people and if you're one such person I would see no point to >>> elaborating and arguing the problem further. >> Self-contradictory statements are false in a consistent universe. Let's >> assume the universe is consistent... > > Mightly nice of you. Or let's not. Makes me no never mind. > Don't makes me no nebbe mine nohows anyway, too...jes' wantin' things be consistent and what-not, so we knows what be de subject matter... >>> However if you do agree what is not universally self contradictory is >>> perforce universally true then all we really have to decide is whether >>> "not not" the "contradiction of contradiction" the "alternative to >>> alternatives" "different from differences" and so on are universally >>> false and if so what the tautological alternatives to such phrases may >>> be and the exhaustive structure and mechanization of truth as well as >>> the demonstration of truth in universal terms would become apparent. >>> >>> ~v~~ >> Not being universally self-contradictory does not make a statement true. >> It just leaves open the possibility... > > No of course it doesn't, Tony. Fact is it leaves open no possibility > whatsoever because every time I ask you what possibility it leaves > open you say none whatsoever per say. > > ~v~~ That's pro se, if you don't mind... 01oo
From: Tony Orlow on 31 Mar 2007 22:11 stephen(a)nomail.com wrote: > In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> stephen(a)nomail.com wrote: >>> In sci.math Brian Chandler <imaginatorium(a)despammed.com> wrote: >>>> stephen(a)nomail.com wrote: >>>>> In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >>>>>> If all other elements in the sequence are a finite number >>>>>> of steps from the start, and w occurs directly after those, then it is >>>>>> one step beyond some step which is finite, and so is at a finite step. >>>>> So you think there are only a finite number of elements between 1 and >>>>> w? What is that finite number? 100? 100000? 100000000000000000? >>>>> 98042934810235712394872394712349123749123471923479? Which one? >>>> None of the ones you've mentioned. Although it is, of course, a >>>> perfectly ordinary natural number, in that one can add 1 to it, or >>>> divide it by 2, its value is Elusive. Only Tony could actually write >>>> it down. >>> These Elusive numbers have amazing properties. According to >>> Tony, there are only a finite number of finite naturals. >>> There exists some finite natural Q such that the set >>> { 1,2,3,4,.... Q} >>> is the set of all finite natural numbers. But what of Q+1? >>> Well we have a couple of options: >>> a) Q+1 does not exist >>> b) Q+1 is not a finite natural number >>> c) { 1,2,3,4, ... Q} is not the set of all finite natural numbers >>> >>> Tony rejects all these options, and apparently has some fourth >>> Elusive option. >>> >>> Stephen >>> > >> Oy. The "elusive" option is that there is no acceptable "size" for N. > > None of the options mention "size" Tony. What does "size" have > to do with a, b or c? > Ugh. Me already tell you, nth one is n, then there are n of them. So easy, even a caveman can do it. Size is difference between. >> That was really hard to figure out after all this time... > > Have you finally figured it out then? I somehow doubt it. > As you have been repeatedly told, for years now, "size" is > not a term used in set theory. Ah I see. Size not matter. Ummm....okay. You tell yourself that. That good for me. You have sister? > > So Tony, yes or no, does there does exist a finite natural Q such > that {1, 2, 3, ... Q } is the set of all finite naturals? > > Stephen > No, there not be place of ending the count. There no biggest, and there no place to call "this big". There always more. Then, after that, even more. Even more bigger than all the things that end. The things don't end. Us make fire and dance around for that. Ugh. Tony
From: Tony Orlow on 31 Mar 2007 22:14
Lester Zick wrote: > On Fri, 30 Mar 2007 12:49:54 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>> This is why science is so useful because you stop arguing isolated >>>>> problems to argue demonstrations instead which subsume those isolated >>>>> problems. There's simply no point to arguing such problems >>>>> individually as to whether "not" is universally true of everything or >>>>> whether there are such things as conjunctions not reducible to "not" >>>>> in mechanically exhaustive terms unless the demonstration itself is >>>>> defective and not true. And just claiming so per say won't cut it. >>>>> >>>> Your "not a not b" has an assumed OR in it. >>> The problem is not whether it has or doesn't, Tony, but how do you >>> know and how can you demonstrate the truth of that claim. I mean there >>> is no visible indication what the relation between A and B is. You >>> might consider the relation between them is "or" but we have no >>> evidence that this conjecture is right and not just rank speculation. >>> I mean there are plenty of people out there who insist that relations >>> between any two items like A and B are theistic, deistic, or even the >>> product of aliens and UFO's. >> >> Please choose true or false, if you didn't do it last time: >> >> a b not a not b >> >> true true true or false? >> true false true or false? >> false true true or false? >> false false true or false? > > Kinda hard to tell what these terms mean, Tony? Are there clues or do > we just wing it? > Yeah, "true" and "false" and "or" are kinda ambiguous, eh?" >>> Consequently it's not my assumption of any relation between A and B >>> but my demonstrations of relations between them that matters. Sure I >>> can assume anything I want. And on previous occasions I certainly have >>> assumed the relation between them was a functional if not explicit or >>> because it seems to me the most plausible mechanical relation likely. >>> But that doesn't mean it's necessarily true. >> You need to define what relation your grammar denotes, or there is no >> understanding when you write things like "not a not b". > > Of course not. I didn't intend for my grammar to denote anything in > particular much as Brian and mathematikers don't intend to do much > more than speak in tongues while they're awaiting the second coming. > Then, what, you're not actually saying anything? >>> However the fact is that given two different things A and B we can >>> combine them with compoundings of "not" and when we do certain >>> conjunctive relations between them fall out the first of which is >>> "and" and the next of which is "or". That's how we can tell what the >>> originary implications between two distinct items is and has to be. >> Not if you assumed OR to begin with. In that case, you're as circular as >> anyone else, and more. Better to build up from true() and false() as >> 0-place predicates. > > Of Christ. Don't you and the zero place predicates wait up for us. > I'll leave the light on. haha >>> But that doesn't mean there is any assumption of "or" between them >>> only that given two distinct things like A and B we can determine any >>> conjunctive relations between them without the implicit assumption of >>> or explicit use of conjuctions. And that means conjunctions and so on >>> are "in here" and not "out there" among distinct things themselves. >> Choose true or false above, and I guarantee you'll see it's the relation OR. > > Of course it is, Tony. I just tried to slip one over on you. OR Brian > OR Virgil OR Stephen OR PD OR David Or Mikey Or someone else > without saying so. > > ~v~~ I think you mean AND. ;) 01oo |